Communication systems, especially wireless communication systems, have become an important portion of modern society. Generally speaking, in a wireless communication system, a base station (e.g., NodeB) establishes radio coverage over a cell, and a terminal (e.g., UE, user equipment) can therefore communicate with the base station by signal transmission through a wireless communication channel between the base station and the terminal. By different communication parameter combinations such as combinations of different modulation schemes and/or coding schemes, the communication channel, involving medium and environment where wireless signals propagate, can be separated to a plurality of physical channels for multiple-access. Some of the physical channels implement downlink channels for transmission from the base station to the terminal; others are allocated as uplink channels for transmission from the terminal to the base station. From another aspect, some of the physical channels are used for data transmission, and others are used for transmission of control information which is used for initiating, managing, handover and/or ending of the communication channel.
In wireless communication systems, the terminal is equipped with a transmitter for forming and sending uplink signals to the base station; in the transmitter, a power amplifier (PA) is adopted for signal transmission. The Peak-to-Average Power Ratio (PAPR) of transmitted waveform limits the maximum transmitted power due to the linearity of the power amplifier. For example, in the third generation (3G) wideband code division multiple access (WCDMA) standard, higher data rates are supported in the uplink direction through the technique of multi-code transmission. Uplink channels such as four E-DPDCHs (Enhanced-Dedicated Physical Data CHannels), one E-DPCCH (Enhanced-Dedicated Physical Control CHannels), one DPCCH (Dedicated Physical Control CHannels), and one HS-DPCCH (High-Speed-Dedicated Physical Control CHannels) can be simultaneously established in the Release 6 specification, and it is known that it leads to higher PAPR, and therefore larger linear range of PA is required to achieve the same root-mean-square (RMS) power since more complicated amplitude modulation schemes are adopted. One way to prevent the higher requirement of PA's linearity is to reduce the requirement of maximum transmitted power for keeping reasonable cost and power consumption at the terminal. Moreover, if the transmitted power exceeds the maximum power with linear characteristic, the nonlinear distortion will appear and form a source of interference for the in-band and out-of-band. In the 3rd Generation Partnership Project (3GPP) technical specification 25.101, a cubic metric (CM) is then defined to determine the amount of 3rd-order inter-modulation distortion and to approximate the PAPR of transmitted signals. Based on the value of CM, the maximum power reduction (MPR) can be determined and the maximum transmitted power can be reduced by a back-off of MPR to minimize the nonlinear effect. Hence, by changing the maximum power dynamically, the PA's linear range can be fully utilized regardless of physical channel configurations and the characteristic of PAPR. The formulas of CM and MPR are:v=rl+j*rQ,vnorm=v/|v|  (eq1)CM_unq=c1*20·log10((vnorm3)rms)+c2CM=CEIL0.5dB(c1*20·log10((vnorm3)rms)+c2)  (eq2)MPR=max(CM−1,0)  (eq3)MPR_unq=max(CM_unq−1,0)where the term v is the transmitted waveform after spreading, scaling by scaling factors, IQ mapping, scrambling, and pulse-shaping filtering; the term CM_unq is an un-quantized CM, and the term MPR_unq is an un-quantized MPR. The term vnorm is the normalized version of the waveform v; the function |x| is the absolute value of x; the function (•)rms is the root-mean-square value of the input argument; and the terms c1 and c2 are two constant depending on the physical channel configuration, including number of physical channels (Nphch), spreading factor, channelization codes, etc. The two constants c1 and c2 also depend on the CM normalization based on the reference waveform. The ceiling function CEIL0.5dB( ) rounds the input argument upwards to the closest multiplication of 0.5 dB.
MPR will be used for the transmitted power control to determine the allowed maximum power. That is, MPR must be calculated before the generation of waveform and highly depends on the physical channel configurations. In 3GPP, the channel configuration could be changed twice per slot (a slot is a predetermined time interval) and thus available processing time of MPR is limited. The CM calculation has to predict the actual CM before forming of the transmitting waveform, and it has to work under tight timing limitation. Another difficulty is that the calculation involves cubic operations and it involves the high dynamic range in the fixed-point implementation.